Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20258607 | C2 | semidirect |
| 2. C2×#20258605 | C2 | semidirect |
| 3. #27131352 | C2 | direct (N × H) |
| 4. C2×#20258596 | C2 | semidirect |
| 5. C2×#20258595 | C2 | semidirect |
| 6. C2×#20258591 | C2 | semidirect |
| 7. C2×C8×D379 | C2 | semidirect |
| 8. C2×SD16×C379 | C2 | semidirect |
| 10. #20258607 | C22 | semidirect |
| 12. #20258605 | C22 | semidirect |
| 20. #20258596 | C22 | semidirect |
| 21. #20258595 | C22 | semidirect |
| 22. #20258591 | C22 | semidirect |
| 24. C8×D379 | C22 | semidirect |
| 27. SD16×C379 | C22 | semidirect |
| 65. C2×C379 | #135 | semidirect |
| 69. C379 | C2×#135 | semidirect |
| 76. C2×SD16 | D379 | semidirect |
| 94. SD16 | C2×D379 | semidirect |
| 137. C2 | #27131352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258607 | 2 |
| C2×#20258605 | 2 |
| #27131352 | 2 |
| C2×#20258596 | 2 |
| C2×#20258595 | 2 |
| C2×#20258591 | 2 |
| C2×C8×D379 | 2 |
| C2×SD16×C379 | 2 |
| C2×#135 | 379 |